Data transmission may rely on the use of a modulation scheme to modulate a carrier wave. Quadrature modulation modulates the carrier wave according to a symbol alphabet defined on a constellation diagram. The constellation diagram is a representation of the interaction between orthogonally defined inphase and quadrature signals (or I- and Q-signals) applied to the carrier wave during transmission.
When the transmitted signal is received, it is necessary to demodulate the signal. To derive the I-signal, the incoming signal is multiplied by a cos(2πfct) signal and to obtain the Q-signal, the incoming signal is multiplied by a sin(2πfct) signal, where fc is the frequency of the carrier wave. The received symbols are determined by the interactions of these received I- and Q-signals.
FIG. 1 illustrates an I/Q plane in which circle 10 represents the location of an ideal received signal, modulated by Quadrature Phase-Shift Keying (QPSK). As the amplitude of each of the symbols is equal and, for each symbol, the I- and Q-signals are orthogonal, the area 10 is a circle.
In practice however, there are a number of factors which affect the amplitude and phase of the I- and Q-signals and which result in a misalignment between these signals. FIG. 2 illustrates an I/Q plane in which ellipse 12 represents the location of a received and processed signal modulated by QPSK. Due to the misalignment between the I- and Q-signals amplitude variations result in a distortion of the radius and phase variations result in I- and Q-axes which are not orthogonal to one another as represented in FIG. 2. Although the I/Q planes illustrated in FIGS. 1 and 2 relate to signals modulated by QPSK, similar IQ misalignment issues exist in other quadrature modulation schemes.
FIG. 3 illustrates a portion of a quadrature receiver 20 of a type known in the art. The receiver 20 includes an antenna 22 for receiving an incoming signal. The received signal is amplified by an amplifier 24 and then follows two parallel signal paths. A local oscillator 30 produces a cos(2πfct) signal which is applied to the incoming signal by mixer 28. A π/2 phase-shifting device 32 alters the signal produced by the oscillator 30 to a sin(2πfct) signal which is then applied to the received signal by mixer 26. The incoming signal multiplied by the cos(2fct) signal is passed through low-pass filter 34 and amplifier 36 to derive the I-signal. The incoming signal multiplied by the sin(2πfct) signal is passed through low-pass filter 38 and amplifier 40 to derive the Q-signal.
Within the receiver 20, imbalances in the amplifiers 36 and 40 introduce an error into the amplitudes of the received symbols, whereas imperfections in phase shifting device 32 introduce an error into the phases of the received symbols.
A misalignment in the I- and Q-signals may increase the bit error rate of the demodulated signal. It is therefore desirable to properly align the I- and Q-signals.
There are at least two methods for realigning misaligned I- and Q-signals. In the first known method, a training or pilot signal is used during a calibration sequence and the received I- and Q-signals are aligned with reference to the calibration. The use of training or pilot signals does not however compensate for additional IQ misalignment which occurs after the calibration sequence has been completed. An example of this type of alignment is disclosed in US 2004/0219884.
In the second known method, referred to as “blind” IQ alignment, only the received signal is available for IQ alignment. At the root of many blind IQ alignment methods lies the realisation that the received signal can be viewed as a combination of an ideal signal (in which the I- and Q-signals are aligned) and a complex conjugate of the ideal signal. In this case certain á priori properties of the signal are used to correct the misalignment.
For example, Valkama, M. and Renfors, M. “Blind Signal Estimation in Conjugate Signal Models with Application to I/Q Imbalance Compensation”, IEEE Signal Processing Letters, Volume 12, No. 11, November 2005 discloses a matrix-representation of received and ideal signals, and their complex conjugates, and the use of matrix algebra to derive an iterative technique to apply a whitening transformation which aligns the I- and Q-signals. However the use of such matrix techniques can be computationally intensive and complex.